Puzzles can arise in ethical theory (as well as decision theory) when infinity is involved. The puzzles arise primarily in theories—such as consequentialist theories—that appeal to the value of actions or states of affairs. Section 1 addresses the question of whether one source of value (such as major aesthetic pleasures) can be infinitely more valuable than another (such as minor gustatory pleasures). An affirmative answer is given by appealing to the notion of lexicographic priority. Section 2 address the question of what morality requires when there are an infinite number of feasible options and no option is maximally valuable? In such cases, it is suggested, morality can demand no more than that we “almost maximize” or (more weakly) that we “satisfice”. Section 3 addresses a puzzle that can arise when time is infinitely long. Is a state of affairs with two units of value at each time more valuable than a state of affairs with one unit at each time (even though both produce infinite amounts of value)? A plausible principle is introduced that answers affirmatively, but it faces certain problems. Section 4 addresses a puzzle that can arise when time is finite but infinitely divisible.